The long term time dependence of a frequency source's
frequency is often called frequency aging. Since other long term changes
can occur, such as changes in the elements of the equivalent circuit of
a crystal resonator, and in a crystal oscillator's input power ("input
power aging" is defined in MIL-O-55310 [1]), clarity of expression requires
that the particular parameter of interest be specifically stated. In the
remainder of this paper, "aging" will mean frequency aging, unless otherwise
specified.

"Aging" and "drift" have occasionally been used interchangeably
in the frequency control literature. However, in 1990, recognizing the
"need for common terminology for the unambiguous specification and description
of frequency and time standard systems," the CCIR adopted a glossary of
terms and definitions .

According to this glossary, aging is "the systematic change
in frequency with time due to internal changes in the oscillator." Added
to the definition is: "Note - It is the frequency change with time when
factors external to the oscillator (environment, power supply, etc.) are
kept constant." Drift is defined as "the systematic change in frequency
with time of an oscillator." Drift is due to aging plus changes in the
environment and other factors external to the oscillator. Aging is what
one specifies and what one measures during oscillator evaluation. Drift
is what one observes in an application. For example, the drift of an oscillator
in a spacecraft is due to (the algebraic sum of) aging and frequency changes
due to radiation, temperature changes in the spacecraft, and power supply
changes.

The CCIR definitions of aging and drift are now incorporated
into the military specifications for crystal oscillators, MIL-O-55310 [1],
and have been recommended by the IEEE Standards Coordinating Committee
27 on Time and Frequency for inclusion in the next edition of the IEEE
Standard Dictionary of Electrical and Electronics Terms.

Random changes of frequency with time, called short term
stability (or, more correctly, short term instability), are characterized
in the time domain by the two-sample deviation (also called the square-root
of the Allan variance), and in the frequency domain by the various measures
of phase noise, as defined in IEEE Standard 1139-1988 [3].

The very accurate and precise measurement of frequency
allows the observation of very small changes in a resonator. It is generally
true that the crystal resonance frequency is a more sensitive measure of
the state of the resonator system than other measurements that can be made.
It has therefore been very difficult to apply measurements other than frequency
to studies of the nature of the aging process, particularly for low-aging
devices.

Many aging measurements have been reported, but few have
included a detailed scientific or statistical study of the aging processes.
Our understanding of resonator aging processes is often based on indirect
evidence gained from other fields (such as material science, and the science
of solid surfaces), and on process developments that seemed "sensible"
for general reasons, and which were followed by an evaluation of the resulting
aging. For high aging rate resonators, advanced surface science measurements
seem to support the use of the "sensible" processes by qualitatively correlating
with the measured aging.

The "sensible" processes generally include suitable crystal
surface preparation, high level of cleanliness during assembly of the resonator,
reasonably well controlled crystal mounting and processing, and hermetically
sealing the resonator into a clean enclosure. High temperature in-process
baking is often used at some stage of resonator fabrication, such as after
mounting, or before final frequency adjustment or sealing. Sometimes a
burn-in after sealing is used to "preage" the resonator before shipment,
and to test for processing deviations.

Precision crystal resonators need to be protected from
operating system environments by sealing in an appropriate package. Typically,
these packages have been glass or metal. For these glass or metal packaged
resonators the resulting resonator system is very complex, in different
ways. Mechanical, chemical, and electrical interactions between the package,
the enclosed materials, and the resonator all can cause aging.

In a crystal oscillator, in addition to the aging of the
resonator, aging of some of the electrical elements (for example, series
inductance or load capacitance) can also change the oscillator's frequency.
Changes in the shape and configuration of the metal leads, and deformation
of circuit boards and enclosures can also produce aging.

Some of the aging of crystal filters is probably associated
with the aging of associated electrical elements. Otherwise, crystal filters
are subject to the same aging processes as other types of resonators.

The following sections of this paper contain discussions
and references to published reports on the topics that are relevant to
our understanding of the aging of resonators, crystal oscillators, and
crystal filters. The emphasis is on reviewing aging processes, and the
literature since 1983. The pre-1983 literature was reviewed by Gerber [4].